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A rational model of the surface swept by a curve *
Author(s) -
Johnstone John K.,
Williams James P.
Publication year - 1995
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.1995.cgf143_0077.x
Subject(s) - bézier curve , surface (topology) , interpolation (computer graphics) , curve fitting , mathematics , position (finance) , representation (politics) , orientation (vector space) , geometric modeling , linear interpolation , computer science , geometry , algorithm , artificial intelligence , mathematical analysis , polynomial , image (mathematics) , statistics , finance , politics , political science , law , economics
This paper shows how to construct a rational Bezier model of a swept surface that interpolates N frames (i.e., N position/orientation pairs) of a fixed rational space curve c(s) and maintains the shape of the curve at all intermediate points of the sweep. Thus, the surface models an exact sweep of the curve, consistent with the given data. The primary novelty of the method is that this exact modeling of the sweep is achieved without sacrificing a rational representation for the surface. Through a simple extension, we also allow the sweeping curve to change its size through the sweep. The position, orientation, and size of the sweeping curve can change with arbitrary continuity (we use C 2 continuity in this paper). Our interpolation between frames has the classical properties of Bezier interpolation, such as the convex hull property and linear precision. This swept surface is a useful primitive for geometric design. It encompasses the surface of revolution and extruded surface, but extends them to arbitrary sweeps. It is a useful modeling primitive for robotics and CAD/CAM, using frames generated automatically by a moving robot or tool.